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Earth's Outer Radiation Belt is a harsh radiation environment trapped by the geomagnetic field. This region is occupied by plasma that has a high-energy tail - i.e. where there are more high-energy electrons present than are expected from the ambient number density and temperature. Some of these electrons travel at a significant fraction of the speed of light, posing a significant environmental hazard to our most useful communications, defence and navigational satellites. Earth's radiation environment is highly variable in response to variability in the solar wind, but the mechanisms that create the variability are not fully understood. I will discuss a range of competing physical mechanisms that fashion the Earth's Radiation Belts, discuss the pros and cons of traditional theoretical approaches to the problem, and display some of our group’s new research insights and directions.